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ThreeDimensional Grid Drawings with SubQuadratic Volume
, 1999
"... A threedimensional grid drawing of a graph is a placement of the vertices at distinct points with integer coordinates, such that the straight linesegments representing the edges are pairwise noncrossing. A O(n volume bound is proved for threedimensional grid drawings of graphs with bounded ..."
Abstract

Cited by 18 (12 self)
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A threedimensional grid drawing of a graph is a placement of the vertices at distinct points with integer coordinates, such that the straight linesegments representing the edges are pairwise noncrossing. A O(n volume bound is proved for threedimensional grid drawings of graphs with bounded degree, graphs with bounded genus, and graphs with no bounded complete graph as a minor. The previous best bound for these graph families was O(n ). These results (partially) solve open problems due to Pach, Thiele, and Toth (1997) and Felsner, Liotta, and Wismath (2001).